Yes it should

I think that the use of the sperm of a dead spouse should be illegal without consent. It violates the rights of people. If a person wants to save sperm so that their spouse or partner can use it to make a baby in the case of them dying, then that is fine. But to do so without consent would be wrong.

Yes without consent

If the spouse dies and never gives consent then yes it should be illegal to use. Typically any time a spouse gives sperm there are forms they must fill out that include what happens upon death. If the forms state something then follow the forms, if there are no forms then air on the side of caution and destroy the sperm.

They have rights as a representative.

No, the use of sperm of a dead spouse should not be illegal without consent, because the spouse usually retains consent for the deceased spouse. The spouse usually has the right to settle all of the other affairs of the dead spouse, they should be allowed to decide this too. Under no circumstance should a woman be allowed to receive social security or public assistance for a child purposefully conceived after a spouse's death.

The existence of sperm donation is implied consent.

Consent from whom, exactly? If the spouse is dead, it's not like he can be dug up to agree or disagree with the action. I think that the fact that such a sperm donation exists from a dead spouse in the first place is an affirmative answer that consent was provided pre-death.

No Need To Oversee

I do not see any reason to waste taxpayer money making laws about the use of a dead spouses sperm. I'm sure this probably is quite uncommon and rarely comes up and when it does, I doubt there are many people aware of the situation and adamantly complaining. I do not think it would serve our best interest to waste time making laws that would apply to so few citizens.